Let q=ph be an odd prime power and e be an integer with 0β€eβ€hβ1. e-Galois self-orthogonal codes are generalizations of Euclidean
self-orthogonal codes (e=0) and Hermitian self-orthogonal codes
(e=2hβ and h is even). In this paper, we propose two general
methods of constructing several classes of e-Galois self-orthogonal
generalized Reed-Solomn codes and extended generalized Reed-Solomn codes with
2eβ£h. We can determine all possible e-Galois self-orthogonal maximum
distance separable codes of certain lengths for each even h and odd prime
number p.Comment: 18 pages, 9 table